(CNN) -- A Saudi group linked to al Qaeda claimed responsibility early Tuesday for the attack on the U.S. Consulate in Jeddah, Saudi Arabia, in which at least five employees and four attackers were killed.

The claim of responsibility was posted on several Islamist Web sites often used by militants. Its authenticity could not be immediately verified.

A U.S. State Department official told CNN that al Qaeda was suspected in the attack.

Asked who the gunmen were, the Saudi Interior Ministry official said they were "wanted" but it was unclear if they were al Qaeda members.

Saudi forces killed three of the gunmen and captured two others, both of whom were wounded, the Saudi Interior Ministry said. One of gunmen later died, and the other gunman was in critical condition, a Saudi source said Tuesday.

Five consular employees -- four local staff members and a contract guard -- were also killed. Four other local staff members were injured and recovering in hospitals, U.S. officials said.

The group that claimed responsibility called itself the Qaeda al Jihad in the Arabian Peninsula.

In the Internet post, the group said, "this operation comes as part of several operations that are organized and planned by al Qaeda as part of the battle against the crusaders and the Jews, as well as part of the plan to force the unbelievers to leave the Arabian Peninsula."

The group said its fighters "managed to enter one of the crusaders' big castles in the Arabian Peninsula and managed to enter the American consulate in Jeddah, in which they control and run the country."

It said the fighters killed nine employees of the consulate, including two Americans, and seven Saudi soldiers.

The U.S. Embassy said no Americans were killed or seriously injured.

The group said two of its fighters were killed and that others escaped unharmed.

The U.S. Embassy in Riyadh, as well as the consulates in Jeddah and Dhahran, will be closed Tuesday because of the incident, according to a warden's message distributed to Americans living in Saudi Arabia.

The message also encourages Americans to "exercise utmost security precautions" in the wake of the attack.

In Washington, President Bush said the incident showed "terrorists are still on the move" trying to get the United States to leave Saudi Arabia and Iraq.

The Interior Ministry said the militants threw explosives at two gates of the sprawling, walled consulate and then entered, exchanging fire with guards.

A senior Saudi official in Washington said an unknown number of third-country nationals who work at the consulate were taken hostage for a time. Some suffered wounds but all were released. A U.S. Embassy spokeswoman said no Americans had been taken hostage.

The Saudi official said they believe a grenade was "thrown in as a diversion." The attackers "stormed into part of the consulate" known as the visa section, where they took the third-country nationals hostage.

A reporter who went to the scene, Mohammed Al-Khereiji of the newspaper Asharq al-Awsat, said that the attackers entered through the south gate, where mail is delivered to the consulate. He said grenades were used and a fire broke out in the compound but was later extinguished.

A senior Bush administration official said there was gunfire, an explosion and then more gunfire as the attack was launched about 11:15 a.m. (3:15 a.m. ET).

In April, the State Department ordered "nonemergency employees and all dependents of the U.S. Embassy Riyadh and Consulates General Jeddah and Dhahran ... to leave the country," because of security concerns, and urged Americans to defer travel to the kingdom.

As recently as August, a vehicle from the U.S. Consulate in Jeddah was hit by gunfire from a single assailant while driving in the city. The two occupants of the vehicle -- the driver and a consulate American employee, were not injured in the attack.

Al Qaeda-led suicide attacks struck Riyadh housing compounds in May and July of 2003, killing 40 people, most of them Muslims.